Question

An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image. Draw the ray diagram.

Answer 1

The image formed by the convex mirror at a distance of
`\(6 (2)/(3)\)`cm from the mirror is virtual, diminished, and upright.

Step-by-step explanation:

When an object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm, we can determine the position and nature of the image using the mirror formula:

`\((1)/(f) = (1)/(v) + (1)/(u)\)`

Here, f is the focal length of the mirror, v is the image distance, and u is the object distance.

Given that u = -10 cm (for a convex mirror, the object distance is taken as negative), and f = 15 cm, we can calculate v using the formula:

`\((1)/(15) = (1)/(v) - (1)/(10)\)`

Solving for v:

`\((1)/(v) = (1)/(15) + (1)/(10)\)`

`\((1)/(v) = (2)/(30) + (3)/(30)\)`

`\((1)/(v) = (5)/(30)\)`

v = 30/5

v =
`6 (2)/(3)\) cm`

Hence, the image is formed at
`\(6 (2)/(3)\)` cm from the mirror. Convex mirrors always produce virtual, erect, and diminished images regardless of the object's position, thus confirming that the image is virtual, diminished, and upright. This is due to the fact that convex mirrors diverge light rays and produce images that are smaller in size than the actual object. A ray diagram can illustrate how the image is formed behind the mirror at the calculated distance, showing the virtual and diminished nature of the image.